Rosser's theorem

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This article is about a theorem in number theory. For Rosser's technique for proving incompleteness theorems, see Rosser's trick. For Gödel–Rosser incompleteness theorems, see Gödel's incompleteness theorems. For the Church-Rosser theorem of λ-calculus, see Church-Rosser theorem.

In number theory, Rosser's theorem was proved by J. Barkley Rosser in 1938. Its statement follows.

Let pn be the nth prime number. Then for n ≥ 1

p_n > n \cdot \ln n.

This result was subsequently improved upon to be:

 p_n > n \cdot(\ln n + \ln(\ln n) - 1). (Havil 2003)

See also[edit]

References[edit]

  • Rosser, J. B. "The nth Prime is Greater than n ln n". Proceedings of the London Mathematical Society 45, 21-44, 1938.

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